Minimal δ(2)-ideal Lagrangian submanifolds and the quaternionic projective space.

We construct an explicit map from a generic minimal δ (2) -ideal Lagrangian submanifold of C n to the quaternionic projective space H P n − 1 , whose image is either a point or a minimal totally complex surface. A stronger result is obtained for n = 3 , since the above mentioned map then provides a one-to-one correspondence between minimal δ (2) -ideal Lagrangian submanifolds of C 3 and minimal totally complex surfaces in H P 2 which are moreover anti-symmetric. Finally, we also show that there is a one-to-one correspondence between such surfaces in H P 2 and minimal Lagrangian surfaces in C P 2. [ABSTRACT FROM AUTHOR]